79 Cougar XR7 Starting Problem

I have a 79 Cougar XR7 with a 351 Windsor with an elect choke. The trouble we are having starting the engine is that when cranking the engine starts but as soon as you let off the key the engine immediatly shuts off. Although if you remove the cord that sends juice to the starter after engine starts and holding the key to "Start" position the car will stay running.

We can't find out what the problem is. Any help will be grateful.